Average and Marginal Cost Functions

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7.3.1 of The Economy 1.0 & The Economy #1

Microeconomics

Year 1

Own Work

Unit 7

#4

Last updated 2:44 PM on 5/12/26
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Given that the total cost function is C(Q), give some properties of it?

-Q is a continuous variable, meaning it can take any positive number, in theory of course

-C’(Q) > 0, meaning it slopes upwards.

-C’’(Q) > 0, meaning it is accelerating upwards.

2
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Given C(Q) is the total cost function, what is the average cost function? Give some properties of it.

-Average cost found by total cost divided by output. Thus:

-The slope of the AC falls and then increases thereafter.

<p>-Average cost found by total cost divided by output. Thus: </p><p>-The slope of the AC falls and then increases thereafter. </p>
3
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Given C(Q) is the total cost function, what is the marginal cost function?

-Very simple. And we have stated this is an upward sloping line.

<p>-Very simple. And we have stated this is an <em>upward sloping line. </em></p>
4
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How can we prove that MC - AC always has the same sign as the slope of the AC curve?

-Differentiating the average cost function: C(Q)/Q with respect to Q, and substituting MC = C’(Q) and C(Q) = Q x AC, we get this.

-Because Q>0, the slope of the AC curve will always have the same sign as MC - AC.

<p>-Differentiating the <em>average cost </em>function: C(Q)/Q with respect to Q, and substituting MC = C’(Q) and C(Q) = Q x AC, we get this. </p><p>-Because Q&gt;0, the slope of the AC curve will <em>always </em>have the same sign as MC - AC. </p>